ABG Corporation has the following dividend forecasts for the next three years:

Year	Expected Dividend
1	$	.25
2	$	.50
3	$	1.25

After the third year, the dividend will grow at a constant rate of 5% per year. The required return is 10%. What is the price of the stock today?

Multiple Choice

$17.40

$18.70

$21.30

$26.25

$27.50

To determine the price of the stock today (P₀), we need to calculate the present value of the expected dividends for the first three years and the present value of the stock price at the end of the third year. The latter value is based on the dividends growing at a constant rate from Year 4 onwards.

### Step 1: Calculate the present value of dividends for Years 1, 2, and 3.

Given:
- Year 1 dividend ($D_1$) = $0.25
- Year 2 dividend ($D_2$) = $0.50
- Year 3 dividend ($D_3$) = $1.25
- Required return ($r$) = 10% or 0.10

The present value of each dividend is calculated using the formula:

\[
PV(D_t) = \frac{D_t}{(1 + r)^t}
\]

#### Year 1:
\[
PV(D_1) = \frac{0.25}{(1 + 0.10)^1} = \frac{0.25}{1.10} \approx 0.227
\]

#### Year 2:
\[
PV(D_2) = \frac{0.50}{(1 + 0.10)^2} = \frac{0.50}{1.21} \approx 0.413
\]

#### Year 3:
\[
PV(D_3) = \frac{1.25}{(1 + 0.10)^3} = \frac{1.25}{1.331} \approx 0.939
\]

### Step 2: Calculate the price of the stock at the end of Year 3 (P₃).

After Year 3, the dividends grow at a constant rate of 5%. The stock price at Year 3 can be calculated using the Gordon Growth Model:

\[
P_3 = \frac{D_4}{r - g}
\]

Where:
- $D_4$ = Dividend in Year 4 = $D_3 \times (1 + g) = 1.25 \times 1.05 = 1.3125$
- $r$ = Required return = 0.10
- $g$ = Growth rate = 0.05

\[
P_3 = \frac{1.3125}{0.10 - 0.05} = \frac{1.3125}{0.05} = 26.25
\]

Now, calculate the present value of $P_3$:

\[
PV(P_3) = \frac{26.25}{(1 + 0.10)^3} = \frac{26.25}{1.331} \approx 19.72
\]

### Step 3: Add the present values of the dividends and the stock price.

\[
P_0 = PV(D_1) + PV(D_2) + PV(D_3) + PV(P_3) \approx 0.227 + 0.413 + 0.939 + 19.72 = 21.30
\]

Thus, the price of the stock today is **$21.30**.

### Answer:
**$21.30**

---

Would you like to delve deeper into any part of the calculation or have further questions?

### Related Questions:
1. How would the price change if the growth rate increased to 6%?
2. What if the required return was 12% instead of 10%?
3. How is the Gordon Growth Model different from other valuation methods?
4. What happens to the stock price if dividends are expected to grow indefinitely at a lower rate than 5%?
5. Can the Gordon Growth Model be used for companies that do not pay dividends?

### Tip:
When calculating the present value of future cash flows, always ensure to adjust for the timing and magnitude of each cash flow to obtain an accurate valuation.

ABG Corporation has the following dividend forecasts for the next three years: Year 1: $0.25, Year 2: $0.50, Year 3: $1.25. After the third year, the dividend will grow at a constant rate of 5% per year. The required return is 10%. What is the price of the stock today? Multiple Choice: $17.40, $18.70, $21.30, $26.25, $27.50

Learn how to calculate the current stock price of ABG Corporation given expected dividends for the next three years and a 5% constant growth rate thereafter. This detailed solution involves the present value of dividends, the Gordon Growth Model, and a 10% required return. Ideal for finance students.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation